Exploring Ductility in Dental Ceramics

Abstract

Two damage regimes—“brittle” and “ductile”—have been identified in the literature on ceramic grinding, machining, grit blasting, and wear. In the brittle regime, the damage mechanism is essentially crack formation, while in the ductile region, it is quasiplasticity. Onset of the brittle mode poses the greater threat to strength, so it becomes important to understand the mechanics of ductile–brittle thresholds in these materials. Controlled microcontact tests with a sharp indenter are employed to establish such thresholds for a suite of contemporary computer-aided design/computer-aided manufacturing dental ceramics. Plots of flexural strength S versus indentation load P show a steep decline beyond the threshold, consistent with well-established contact mechanics relations. Threshold dimensions occur on a scale of order 1 µm and contact load of order 1 N, values pertinent to practical grit finishing protocols. The ductile side of ceramic shaping is accessed by reducing grit sizes, applied loads, and depths of cut below critical levels. It is advocated that critical conditions for ductile shaping may be most readily quantified on analogous S(P) plots, but with appropriate machining variable (grit size, depths of cut, infeed rate) replacing load P. Working in the ductile region offers the promise of compelling time and cost economies in prosthesis fabrication and preparation.

Introduction

Ceramics are finding ever increasing applications as restorative materials for dental prostheses (Denry and Kelly 2008, 2014; Kelly and Benetti 2011; Rekow et al. 2011; Pieralli et al. 2017; Sulaiman et al. 2017; Zhang and Kelly 2017; Zhang and Lawn 2018). But ceramics are brittle and notoriously unforgiving: finishing, polishing, and bonding often involve procedures that generate strength-degrading microcrack damage in the subsurface (Xu and Jahanmir 1994; Xu et al. 1996; Kosmač et al. 1999; Coldea et al. 2013). Computer-aided design (CAD)/computer-aided manufacturing (CAM) machining (milling) (Denry 2013), intraoral and extraoral adjustments (grinding) (Rodrigues et al. 2018), and surface modifications (grit blasting) (Zhang et al. 2004) are prime cases in point. Clinical studies confirm that attendant cracking associated with milling and grinding damage in dental ceramics can be a principal source of failure (Krämer et al. 1999; Belli et al. 2016). An in vitro study of hand grinding with a 75-µm diamond grinding disc produced cracks ~100 µm deep in a lithia glass–ceramic and a feldspathic ceramic, with resultant strength reductions 50% and 30%, respectively (Curran et al. 2017). Any guidelines that can ameliorate the deleterious effects of microcrack damage offer the potential for improved clinical performance by extending the lifetime of ceramic prostheses. Ideally, establishing conditions where the damage process is ostensibly ductile rather than brittle without sacrificing economy in prosthetic preparation would appear to be a holy grail in bioceramic manufacturing.

Essentially, CAD/CAM milling, handpiece grinding, and abrasive grit blasting involve multiple microcontact events with sharp abrasive particles. It is fundamentally a contact problem on a micrometer scale, quantifiable by well-documented indentation mechanics (Lawn and Wilshaw 1975; Ostojic and McPherson 1987; Cook and Pharr 1990). In fine-grain ceramic materials, such indentations typically generate attendant cracks that extend radially outward and downward from the contact zone. These cracks readily propagate to failure in subsequent tensile loading. Ceramics are particularly vulnerable to fracture processes in multiple, repetitive contact events—fatigue (Zhang et al. 2013). However, even in the most brittle of materials, there exist threshold loads below which embryonic cracks are subsumed within a plastic contact zone, the so-called ductile region (Arora et al. 1979; Lawn and Marshall 1979; Lawn et al. 2021). This is leading to a strong movement toward ductile grinding in manufacturing, whereby contact loads and grit sizes are scaled back in order to operate in this subthreshold region (Bifano et al. 1991; Malkin and Guo 2007; Huang et al. 2021). If this principle can be extended to the manufacture of dental ceramic prostheses, clinicians may no longer need to concern themselves with premature failures from strength-limiting defects.

In this article, we explore the conditions for brittle–ductile transitions in a suite of topical dental ceramics. Indentation tests with a commercial sharp indenter are used to establish the existence of threshold behavior in each of these ceramics. Then flexural strength tests on indented specimens are conducted to highlight the nature of the brittle–ductile transition and to quantify the structural integrity of each dental material. The interplay between microcracks induced during finishing and intrinsic defects associated with the material microstructure is outlined. Implications concerning optimization of milling, grinding, and sandblasting will be considered.

Materials and Methods

Preparation of Dental Ceramic Specimens

Five commercial restorative materials representing 3 classes of dental ceramics were selected for comparative study: 2 zirconias, 3 mol% yttria-stabilized tetragonal zirconia (3Y-TZP) and 5 mol% partially stabilized zirconia (5Y-PSZ) (Zpex and Zpex Smile; Tosoh Corp.); 2 glass–ceramics (G-C), lithia based (IPS e.max CAD; Ivoclar Vivadent) and leucite reinforced (IPS Empress CAD; Ivoclar Vivadent); and a feldspathic ceramic (feldspar) (Vitablocs Mark II; Vita Zahnfabrik). 3Y-TZP and 5Y-PSZ discs were cut from presintered rods and then sintered at 1,530°C and 1,450°C, respectively, for 2 h in a box furnace in air (Lindberg/Blue M; Thermal Scientific), according to manufacturer’s specifications. Blocks of lithia G-C, leucite G-C, and feldspar were shaped into cylinders with a diamond hole saw and sliced with a diamond blade (IsoMet 1000; Buehler). The lithia G-C discs were crystallized at 850°C in a vacuum furnace (EP5000; Ivoclar Vivadent). All discs were leveled with a 15-µm diamond pad on both sides, followed by diamond polishing to a 1-µm surface finish. The final dimensions of all test specimens were Ø12 × 1 mm (n = 60).

The microstructures of the different ceramics were examined on 3Y-TZP and 5Y-PSZ (thermally etched), lithia G-C and leucite G-C (chemically etched), and feldspar (as-polished) surfaces using scanning electron microscope (SEM) (Quanta 600 FEG Mark II Environmental SEM; Thermal Fisher Scientific). Representative mechanical properties and controlling microstructural scales listed in the Table are ascertained from current tests: toughness directly from strengths of indented specimens in flexure tests (n > 20), grain size by the linear intercept method in SEM images (Wurst and Nelson 1972), and intrinsic strength from flexure tests on unindented specimens (n = 30).

Controlled Microcontact Damage

Microcontact damage was induced into the center of each specimen using Vickers diamond pyramid indenters. A microhardness test machine (Zwick 31212; ZwickRoell) was used to apply loads from 0.1 to 7 N and a macrohardness machine (Phase II+; Phase II Machine & Tools) for loads 10 to 100 N. Vickers indenters were employed because they constitute the most widely documented commercially available configuration. Immediately after indentation, the contact sites were examined in an optical microscope (Nikon Eclipse LV150N; Nikon) and images acquired. Plastic impression and radial crack diagonals were measured to an accuracy of ±0.5 µm. A drop of silicone oil was then applied to the contact site to minimize any subsequent moisture-enhanced subcritical crack growth (Wiederhorn 1967) prior to and during ensuing strength testing.

Flexural Strength Test

A piston-on-three-ball configuration was used to determine disc specimen strengths, with hardened steel balls supporting the specimen on an 8-mm diameter circle. The discs were oriented with the previously emplaced indentations centered on the lower surface. A flat hardened steel piston of diameter 1.4 mm applied an axial load at the upper surface, immediately above the indent site. The fracture tests were carried out in a universal machine (Instron 5566; Instron) using a 1-kN load cell at 1 mm/min crosshead speed. Critical loads to failure were recorded and corresponding flexural strengths calculated according to ISO 6872/2015. The fractured pieces of each specimen were reassembled and the lower surfaces observed in an optical microscope to determine whether fracture initiated at or away from the indentation site.

Results

Ceramic Microstructures

Representative SEM micrographs of select dental ceramic surfaces are shown in Figure 1. The zirconias have fine equiaxed microstructures with strong grain boundaries and biphasic tetragonal and cubic phases (3Y-TZP: 70 vol% t-ZrO₂, 30 vol% c-ZrO₂; 5Y-PSZ: 30 vol% t-ZrO₂, 70 vol% c-ZrO₂) (Yan et al. 2018). The lithia G-C consists of 70 vol% elongate crystallites in a glassy matrix, with isotropic orientation (Zhang and Kelly 2017). The leucite G-C contains ~35 vol% round-edged crystallites in a glassy matrix. The feldspar contains ~32 vol% coarse crystallites in a glass matrix but on a coarser scale (Borrero-Lopez et al. 2019). The size of critical microstructural flaws is well known to govern the strength of polycrystalline ceramics (Lawn 1993).

Figure 1.

Microstructures of dental ceramics used in this study. (A) 3 mol% yttria-stabilized tetragonal zirconia (3Y-TZP). (B) 5 mol% partially stabilized zirconia (5Y-PSZ). (C) Lithia glass–ceramics (G-C). (D) Leucite G-C. (E) Feldspar.

Indentation Crack Patterns

Figure 2 shows images of indentations in each of the selected dental ceramics, taken at a common intermediate contact load P = 5 N. At this load, radial corner cracks extend from the impressions in all materials except 3Y-TZP. These radial cracks are well formed, near symmetrical with respect to the square impressions, typical of fine-grain materials in the brittle region. The cracks are longer in the materials with lower toughness values. While no such cracks are visible in the 3Y-TZP, indicating indentation in the subthreshold ductile region, they become apparent at higher loads. Comparison between the 2 zirconia ceramics in Figure 2 highlights a diminished brittleness in 3Y-TZP relative to 5Y-PSZ.

Figure 2.

Optical microscope images of Vickers indentations at load 5 N in dental ceramics. At this load, well-formed radial cracks are observed at the impression corners for all materials except 3 mol% yttria-stabilized tetragonal zirconia (3Y-TZP), indicating subthreshold contact in the latter case.

These trends are more rigorously quantified in Figure 3. This figure plots characteristic indentation diagonals 2a (open symbols) and 2c (closed symbols) as a function of load P for all materials. Each point in this data set is the average of diagonal corner-to-corner (impression) and tip-to-tip (crack) measurements in the 2 orthogonal directions for each indentation. Solid lines are best fits to the reduced form of established contact relations (Lawn and Cook 2012):

Figure 3.

Plots of characteristic hardness impression dimension a and radial crack dimension c as function of preindentation load P. Crossover of a(P) and c(P) functions delineates transition between “brittle” and “ductile” regions. Lines through the data points are fits to equation (1). This figure is available in color online.

$$P=\alpha H{a}^2,$$ (1a)

$$P=\beta T{c}^{3/2},$$ (1b)

where H is hardness, T is toughness, and α and β are coefficients. Strictly, the coefficient β in equation (1b) has a functional dependence on the ratio E/H of elastic modulus to hardness, but that dependence is relatively modest (Lawn et al. 1980; Lawn and Cook 2012). Since the a(P) and c(P) functions in equation (1) have different exponents (i.e., slopes 1/2 and 2/3 on the logarithmic plots), the fitted lines for each material cross each other. The intersection point delineates transition from the brittle region to the ductile region as the contact dimension falls below the threshold for crack initiation.

Strength Degradation

The lower surfaces of each indented ceramic specimen in the flexure strength tests were examined to ascertain fracture origins. At the lower loads, the failure paths did not intersect the indentations, indicating failure from intrinsic microstructural flaws. At higher loads, the crack paths passed directly through the indentation sites, confirming failure from dominant radial cracks. All specimens in the latter category exhibited diminished strengths.

The data set in Figure 4 plots strength S versus indentation load P from the flexure tests. Points are strengths of individual preindented specimens, with filled symbols representing fracture origins from the indentation sites and unfilled symbols origins away from these sites. The shaded box and horizontal solid line at left of each plot represents mean and standard deviations for strengths S₀ of nonindented, as-polished specimens, corresponding to breaks from intrinsic microstructural flaws. Critical flaw sizes c_f were evaluated from the classical Griffith strength relation (Lawn 1993):

Figure 4.

Strength S as a function of preindentation load P from flexure tests. Filled symbols represent failure origins at indentation sites and unfilled symbols failures away from these sites. Boxes at left vertical axis are means and standard deviations for base tests on specimens without indentations. Lines through the data points are fits to equation (2). This figure is available in color online.

$$S_0=T/\psi {c_{\text{f}}}^{1/2},$$ (2a)

with ψ a geometrical coefficient. Inserting ψ = π^1/2 for ideal straight-fronted cracks into equation (2a) (Lawn 1993), evaluations of c_f are included for each material in the Table. The inclined line through the filled symbols is a best fit to the reduced strength relation for specimens preindented at load P (Lawn and Cook 2012):

$$S_P=T^{4/3}/{\eta }^{4/3}{P}^{1/3},$$ (2b)

Table.

Mechanical Properties, Grain Sizes, Critical Flaw Sizes, and Threshold Loads of Dental Ceramics.

Material	Manufacturer	Toughness T (MPa.m1/2)	Hardness H (GPa)	Grain Size l (µm)	Strength S0 (MPa)	Flaw Size cf (µm)	Critical Load P* (N)
3 mol% Yttria-stabilized tetragonal zirconia polycrystal (3Y-TZP)	Zpex (Tosoh)	5.9 ± 0.5 (n = 23)	13.7 ± 0.2	0.54 ± 0.04	878 ± 92 (n = 30)	4.7	3.3
5 mol% Yttria partially stabilized zirconia (5Y-PSZ)	Zpex Smile (Tosoh)	3.1 ± 0.2 (n = 31)	13.2 ± 0.2	1.33 ± 0.06	609 ± 133 (n = 30)	2.6	0.7
Lithium disilicate glass–ceramic (lithia G-C)	IPS e.max CAD (Ivoclar Vivadent)	2.1 ± 0.3 (n = 29)	6.3 ± 0.1	0.4 (width) 1.0 (length)	475 ± 84 (n = 30)	2.0	0.4
Leucite-reinforced glass–ceramic (leucite G-C)	IPS Empress CAD (Ivoclar Vivadent)	1.3 ± 0.2 (n = 30)	6.7 ± 0.1	1–5	171 ± 19 (n = 30)	5.9	0.9
Feldspathic ceramic (feldspar)	Vitablocks Mark II (VITA Zahnfabrik)	1.3 ± 0.2 (n = 23)	7.1 ± 0.2	2–18	93 ± 6 (n = 30)	19.8	6.5

with η = 0.88 for Vickers indentations from historical coefficient calibration over a wide range of ceramics (Chantikul et al. 1981). Beyond the radial crack threshold, indentation cracks begin to dominate the intrinsic flaw population. In this context, note that equation (2b) contains no explicit dependence on c_f. The strength falloff in this region is substantial, with slope –1/3 on the logarithmic plots, by an amount approaching an order of magnitude at higher load contacts. At the same time, it is apparent that all ceramics retain their initial strengths while the indentations remain in the subthreshold ductile zone. There is some data scatter in the transition region, indicating inaccuracy in pinpointing the thresholds on logarithmic plots that cover a load range over several orders of magnitude. A shift from brittle to ductile regions at lower contact loads is nonetheless well delineated. We have provisionally used the best fits to the S_P(P) data to deconvolute the toughness values presented in the Table. This was done by calculating the quantity S_PP^1/3 for each filled data point in Figure 4 and using the mean and standard deviation for each material to evaluate T from equation (2b). Note that equation (2b) conveniently circumvents any need to measure crack dimensions.

Discussion

Data Analysis

The materials studied here show characteristic contact damage responses typical of fine-grain brittle ceramics, namely, well-formed Vickers indentations with near-symmetrical radial corner cracks (Fig. 2) and linearities in indentation dimensions and strength data in logarithmic plots (Figs. 3 and 4), in accordance with equations (1) and (2). The microcontact patterns visually highlight a brittle–ductile transition, whereby radial crack embryo becomes subsumed within the central plastic hardness impression below a threshold contact size. This transition is quantified by the intersection of the a(P) and c(P) data sets in Figure 3. Setting a_* = c_* at the crossover point and eliminating load P in equations (1a) and (1b) yields the threshold impression dimension (Lawn and Marshall 1979; Lawn and Cook 2012):

$$a\ast ={(\beta T/\alpha H)}^2.$$ (3)

For the dental ceramic data in the a(P) and c(P) plots, the value of a_* is of order 1 µm for Vickers indenters. As alluded to earlier, the coefficient β in equation (3) is susceptible to material variations in E/H as well as to indenter geometry, but the existence of a brittle–ductile threshold as a microcontact size effect is nevertheless a general phenomenon for ceramics with a high “brittleness index” H/T (Lawn and Marshall 1979; Lawn and Cook 2012).

The threshold behavior is more clearly delineated in the strength data in Figure 4. The filled symbols in these plots, representing specimen breaks from controlled indentation flaws, usefully provide a measure of potential strength degradation in the “brittle” region. As mentioned, fits to these S_P(P) data sets in accordance with equation (2b) afford a means of evaluating effective toughness values. However, it is emphasized that toughness evaluation is a secondary concern here—we include it simply to show consistency with literature values within the data scatter (Zhang et al. 2016; Belli et al. 2018). It is strength S, not toughness T, that is the principal mechanical property of interest in this study. The use of precursor indentations conveniently enables us to delineate the regions of flaw tolerance and intolerance in a systematic manner on the S(P) plots, without ever having to measure crack sizes. The threshold load P = P_* at the crossover between the filled and unfilled data sets in Figure 4 is thereby quantified by setting S_P = S₀ in equation (2b), that is,

$$P\ast =T^4/{\eta }^4{S_0}^3.$$ (4)

Values of P_* calculated from equation (4) included in the Table are of the order 1 N. Given the scatter in the data on the logarithmic load scale over several orders of magnitude, these evaluations are subject to some numerical uncertainty, but the existence of a brittle–ductile transition is unequivocal.

The appearance of intrinsic strength S₀ in equation (4) introduces a microstructural element into the analysis. A lower value of S₀ for any given material extends the data range within the so-called ductile region at P < P_*. Strength S₀ in equation (1) is governed by the Griffith flaw size c_f, which, as seen in the Table, is of the same order as the grain size l. This may explain why the ductile region is relatively expansive for the feldspathic ceramic in Figure 4, even though feldspar is generally considered to be a relatively brittle material: comparison of the data in Figure 4 with those in Figure 3 indicates that indentations may not be entirely crack free immediately to the left of the crossover; it simply means that any such cracks can be dominated by preexisting microstructural flaws in this low-load region.

It is acknowledged that the quantities listed in the Table are determined from controlled indentation protocols and might thus be considered restrictive. Indentations are made with an ideal sharp geometry under near-inert conditions, whereas microcontact events in finishing and grit blasting procedures are generally more complex, with variable grit shapes and sizes, repeated loading, translational motion, overlap of multiple contact sites, and so on. However, tests under well-controlled conditions enable one to establish the generality of threshold microcontact behavior with minimal complication, notably critical dimensions on the micrometer scale and contact loads of order N, and usefully identify and quantify the roles of principal material parameters.

Implications Concerning Clinical Adjustment and Finishing

The fabrication of dental ceramic prostheses is essentially the sum total of a multiplicity of microcontact events, each on the same scale as described in the current controlled indentation tests, albeit with the abovementioned configurational complexities. Shaping, finishing, and grit-blasting processes generally involve surface contact with hard grit particulates, in fixed or loose form. For ceramics, material removal in the brittle region is effected by coalescence of microcracks within and surrounding the contact zone and in the ductile region by more plastic chip formation (Huang et al. 2021; Lawn et al. 2021). Common mechanical preparation processes used in a dental setting include the following:

• Grinding and polishing. Fixed grit in diamond burs on rotary instruments for shaping and finishing. Variables—grit size and shape; rotational speed, applied load, depth of cut, feed rate (Huang et al. 2021).

• Grit blasting. Pressure-fired loose particulates, for surface cleaning and mechanical retention (Zhang et al. 2004). Variables—particle size and shape, airstream pressure, stand-off distance, impact velocity and angle (Finnie 1960).

In relation to ceramic prostheses, initial milling and shaping is most economically carried out in brittle mode (i.e., in the postthreshold contact region), where removal rates are relatively high. This broadly requires coarse, sharp grits and moderate to high contact forces. The downside of operating in this mode is that the strength of the prosthesis can be severely compromised. Defect-free finishing is more effectively accomplished in the ductile mode (i.e., in the subthreshold region), where removal rates are lower but the surface is smoothed out by plastic smearing. Fine grits and relatively low operational forces, along with somewhat more precision engineering practices, are requisite elements. The challenge is to balance superior surface finish against higher operational cost. In the context of Figures 3 and 4, optimization would ideally require the pertinent microcontact events to lie just within the subthreshold zone, that is, within the plateau region of Figure 4, not too far in as to overly diminish the surface removal rate but not too close as to introduce spurious contact fractures. While the indentation data usefully demonstrate the ductile side of dental ceramics and identify the controlling material parameters (e.g., toughness, grain size), it is suggested that practical threshold conditions be quantified on specimens as a function of finishing process and attendant test variables, with any such variable replacing load P on the horizontal axis of strength plots of the kind in Figure 4. This is a ripe area for future research.

Conclusion

1. Controlled indentation tests can be used to determine microcontact thresholds for dental ceramics, in a manner that simulates events in clinical finishing protocols. Above threshold, the contact operates in brittle mode, below threshold in ductile mode.

2. For individual sharp, static contacts, the threshold dimension is of order 1 µm and corresponding threshold load of order 1 N. These values lie in the range of practical finishing processes, albeit dependent on machining, grit-blasting, and milling variables.

3. Dental ceramics have a ductile side, accessed by maintaining microcontact processes in the subthreshold region (i.e., in the domain P < P_* in equation (4) and the Table). From a ductile machining perspective, a high value of P_* is most readily attained in materials with high toughness T (e.g., 3Y-TZP) or large grain size (e.g., feldspathic ceramic).

4. From a materials perspective, while a high value of P_* is desirable for ductile finishing, this has to be balanced against the need of a high intrinsic strength S₀ for survival against occlusal loading during ensuing in vivo function.

Author Contributions

L.M.M. Alves, C.S. Rodrigues, contributed to design, data acquisition, and analysis, drafted and critically revised the manuscript; S. Vardhaman, contributed to data acquisition and analysis, drafted and critically revised the manuscript; C. Saunders, J.M. Schneider, contributed to data acquisition, critically revised the manuscript; B.R. Lawn, contributed to conception, design, data analysis, and interpretation, drafted and critically revised the manuscript; Y. Zhang, contributed to conception, design, data acquisition, analysis, and interpretation, drafted and critically revised the manuscript. All authors gave final approval and agree to be accountable for all aspects of the work.